(a) Show that for motion with uniform acceleration in a straight line, the average…

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

(a) Show that for motion with uniform acceleration in a straight line, the average velocity

\bar v

during a time interval

t

is equal to the arithmetic mean of the initial velocity

u

and the final velocity

v

, i.e.,

\bar v = \dfrac{u+v}{2}

. (b) A motor-car moving in a straight line accelerates uniformly from rest to a speed of

25\,\text{m/s}

10\,\text{s}

. Using the result proved in part (a), calculate: (i) the average speed of the car during this interval, (ii) the distance travelled in these

10\,\text{s}

. (c) Explain why, for non-uniform acceleration, the relation obtained in part (a) does not necessarily hold.